4,165,000

2³ × 5⁴ × 7² × 17

For 4,165,000, the 120 positive divisors have a total of 12,019,590. Removing 4,165,000 leaves 7,854,590, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^3 × 5^4 × 7^2 × 17

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 12,019,590

Proper Divisor Sum 7,854,590

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #4164989 ← → #4165037

Radix Representation

Decimal	4165000
Binary	1111111000110110001000 (22 bits)
Octal	0o17706610
Hexadecimal	0x3F8D88

Divisor Catalog (60 of 120)

1 2 4 5 7 8 10 14 17 20 25 28 34 35 40 49 50 56 68 70 85 98 100 119 125 136 140 170 175 196 200 238 245 250 280 340 350 392 425 476 490 500 595 625 680 700 833 850 875 952 980 1,000 1,190 1,225 1,250 1,400 1,666 1,700 1,750 1,960

Collatz Trajectory (105 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

4,165,000 2,082,500 1,041,250 520,625 1,561,876 780,938 390,469 1,171,408 585,704 292,852 146,426 73,213 219,640 109,820 54,910 27,455 82,366 41,183 123,550 61,775 185,326 92,663 277,990 138,995 416,986 208,493 625,480 312,740 156,370 78,185 234,556 117,278 58,639 175,918 87,959 263,878 131,939 395,818 197,909 593,728 296,864 148,432 74,216 37,108 18,554 9,277 27,832 13,916 6,958 3,479 10,438 5,219 15,658 7,829 23,488 11,744 5,872 2,936 1,468 734

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